Candidate Name Centre Number Candidate Number MATHEMATICS UNIT 1: NON-CALCULATOR HIGHER TIER SPECIMEN PAPER SUMMER 2017

Transcription

1 GCSE MATHEMATICS Specimen Assessment Materials 7 Candidate Name Centre Number Candidate Number 0 GCSE MATHEMATICS UNIT 1: NON-CALCULATOR HIGHER TIER SPECIMEN PAPER SUMMER HOUR 45 MINUTES ADDITIONAL MATERIALS The use of a calculator is not permitted in this examination. A ruler, protractor and a pair of compasses may be required. INSTRUCTIONS TO CANDIDATES Write your name, centre number and candidate number in the spaces at the top of this page. Answer all the questions in the spaces provided in this booklet. Take INFORMATION FOR CANDIDATES You should give details of your method of solution when appropriate. Unless stated, diagrams are not drawn to scale. Scale drawing solutions will not be acceptable where you are asked to calculate. The number of marks is given in brackets at the end of each question or part-question. For Examiner s use only Question Maximum Mark TOTAL 80 Mark Awarded The assessment will take into account the quality of your linguistic and mathematical organisation, communication and accuracy in writing in question 11.

2 GCSE MATHEMATICS Specimen Assessment Materials 8 Formula list Higher tier Area of a trapezium = 1 ( ) 2 a b h Volume of a prism = area of cross section length 4 Volume of a sphere 3 r Surface area of a sphere 3 = 4 r Volume of a cone 3 r h Curved surface area of a cone rl In any triangle ABC, Sine rule: a b c sin A sin B sin C Cosine rule: a b c 2bc cos A Area of triangle 1 sin 2 ab C The Quadratic Equation The solutions of ax 2 + bx + c = 0 where a are given by x 2 b b 4ac 2a Annual Equivalent Rate (AER) i AER, as a decimal, is calculated using the formula 1 1, where i is the nominal n interest rate per annum as a decimal and n is the number of compounding periods per annum. n

3 GCSE MATHEMATICS Specimen Assessment Materials 9 1. Mair either walks, cycles, travels by car or travels by bus to work each day. Her method of travel each day is independent of her method of travel on any other day. The table below shows the probability for three of her methods of travel on any randomly chosen day. Method of travel Walk Bike Car Bus Probability (a) Calculate the probability that, on any randomly chosen day, she walks to work. [2].. (b) What is the probability that, on any randomly chosen day, she either travelled to work by car or by bus? [2].. (c) What is the probability that, in any randomly chosen week, Mair travelled to work by car on the Monday and by bus on the Tuesday? [2]..

4 GCSE MATHEMATICS Specimen Assessment Materials (a) The table below shows some of the values of y = x 2 3x 2 for values of x from 2 to 4. Complete the table by finding the value of y for x = 2. [1] x y = x 2 3x (b) On the graph paper opposite, draw the graph of y = x 2 3x 2 for values of x from 2 to 4. [2] (c) Using your graph, write down the two solutions of the equation x 2 3x 2 = 0. Give your answers correct to 1 decimal place. [1] Solutions are... and... (d) By drawing a suitable line on your graph, write down the two solutions of the equation x 2 3x + 1 = 0. Give your answers correct to 1 decimal place. [3].. Solutions are... and...

5 GCSE MATHEMATICS Specimen Assessment Materials 11 For use with question 2. y x

6 GCSE MATHEMATICS Specimen Assessment Materials (a) Use a ruler and a pair of compasses to construct an angle FGH ˆ of size 30 at point G. [3] F G (b) A regular polygon has interior angles of 135. How many sides does this polygon have? [3]

7 GCSE MATHEMATICS Specimen Assessment Materials 13 (c) Shape A is translated onto Shape B. Which one of the following vectors describes the translation? Circle your answer. [1] (a) Calculate the largest share when 400 is shared in the ratio 1: 2: 5. [2] (b) A price of 63 includes VAT at a rate of 5%. What was the price before VAT was added? [2]

8 GCSE MATHEMATICS Specimen Assessment Materials Circle your answer in each of the following. (a) The value of 2 3 as a fraction in its simplest form is [1] (b) 2 as a recurring decimal is [1] (c) 17 0 is equal to [1]

9 GCSE MATHEMATICS Specimen Assessment Materials A six-sided dice was thrown repeatedly. After every 100 throws, the cumulative number of sixes thrown was recorded. (a) Complete the table below, which gives a summary of the results obtained. [1] Number of throws Number of sixes Relative frequency (b) Draw a relative frequency diagram to show the information given in the table. [1] (c) From the table, which value gives the best estimate for the probability of throwing a six? You must give a reason for your choice. [1] (d) Do you think this is a fair dice? You must give a reason for your choice. [1]

10 GCSE MATHEMATICS Specimen Assessment Materials Find, in standard form, the value of (a) ( ) 3000, [2] (b) ( ) ( ). [2] 8. The diagram shows the first four patterns of a sequence Find an expression for the number of squares in the nth pattern of the sequence. [2]

11 GCSE MATHEMATICS Specimen Assessment Materials On the grid below, draw an enlargement of the given shape using a scale factor of and centre A. 1 2 [3] A

12 GCSE MATHEMATICS Specimen Assessment Materials Given that y is inversely proportional to x 2, and that y = 5 when x = 2, (a) find an expression for y in terms of x. [3] (b) Use the expression you found in (a) to complete the following table. [2] x y

13 GCSE MATHEMATICS Specimen Assessment Materials You will be assessed on the quality of your organisation, communication and accuracy in writing in this question. A cuboid with a volume of 912cm 3 has dimensions 4 cm, (x + 2) cm and (x + 9) cm. Show that x x 210 = 0. Solve this equation and find the dimensions of the cuboid. You must justify any decisions that you make. [9]

14 GCSE MATHEMATICS Specimen Assessment Materials Circle your answer in each of the following. (a) (2a 3 ) 4 is equal to 2a 12 8a 12 16a 7 16a 12 24a 34 [1] (b) Given that h 2 = a 2 + b 2, then b is equal to 2 2 h a h a h 4 a 4 2 ( a h ) h a 2 2 [1]

15 GCSE MATHEMATICS Specimen Assessment Materials (a) Express as a fraction. [2] (b) Find the values of a and b, given that a b [3] a =... b =... (c) Evaluate [2]

16 GCSE MATHEMATICS Specimen Assessment Materials (a) The diagram shows a sketch of the graph y = f(x). The graph passes through the points ( 2, 0) and (6, 0) and its highest point is at (2, 4). y (2, 4) ( 2, 0) O (6, 0) x Sketch the graph of y = f(x + 5) on the axes below. You must indicate the coordinates of its highest point and the coordinates of the points of intersection of the graph with the x-axis. [3] y O x (b) The diagram below on the left shows a sketch of the graph of y = x 2. Sketch the graph of y = x on the axes on the right. You must indicate the coordinates of the point where the curve crosses the y-axis. [2] y y O x O x

17 GCSE MATHEMATICS Specimen Assessment Materials 23 (c) Explain why it is not possible to determine the translation used on the function g(x) in the diagram below. [1] y = g(x) y O x

18 GCSE MATHEMATICS Specimen Assessment Materials The points A, B and C lie on the circumference of a circle. The straight line PBT is a tangent to the circle. AB = AC. CBP ˆ x, where x is measured in degrees. A C T x B P Diagram not drawn to scale Show, giving reasons in your answer, that the size of AB ˆ 1 C, in degrees, is 90 x. 2 [4]

19 GCSE MATHEMATICS Specimen Assessment Materials (a) When Anna shoots an arrow, the probability that she hits the target is 0 3. Each attempt is independent of any previous shot. (i) What is the probability that Anna hits the target for the first time on her third attempt? [3] (ii) Evaluate whether or not there is more than a 50% chance of Anna hitting the target exactly once on her first three attempts. [3] (b) Siôn selects two balls, at random, from a box containing 15 blue balls and 5 red balls. He calculates that the probability of selecting two red balls is What assumption has Siôn made for his answer to be correct? [1]

20